Problem: Simplify the following expression: $\sqrt{63} + \sqrt{28}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{63} + \sqrt{28}$ $= \sqrt{9 \cdot 7} + \sqrt{4 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{7} + \sqrt{4} \cdot \sqrt{7}$ $= 3\sqrt{7} + 2\sqrt{7}$ Finally, simplify by combining the terms. $= ( 3 + 2 )\sqrt{7} = 5\sqrt{7}$